Gravitation - Result Question 34

35. The potential energy of a satellite, having mass $m$ and rotating at a height of $6.4 \times 10^{6} m$ from the earth surface, is

[2001]

(a) $-m g R_e$

(b) $-0.67 m g R_e$

(c) $-0.5 m g R_e$

(d) $-0.33 m g R_e$

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Answer:

Correct Answer: 35. (c)

Solution:

  1. (c) Mass of the satellite $=m$ and height of satellite from earth $(h)=6.4 \times 10^{6} m$.

We know that gravitational potential energy of the satellite at height $h$,

$GPE=-\frac{G M_e m}{R_e+h}=-\frac{g R_e^{2} m}{2 R_e}$

$=-\frac{g R_e m}{2}=-0.5 m g R_e$

(where, $G M_e=g R_e{ }^{2}$ and $h=R_e$ )